xtpcse or xtreg, fe r in panel data where N is not much larger than T

[Simone Tonelli]

Dear Statalists,

I want to estimate several macro-econometric models using country-year panel data testing positive for heteroskedasticity and autocorrelation. For each model, the dataset varies in size as follows:

1) N=26, T=4-20, average T = 16
2) N=23, T=6-21, average T = 16
3) N=16, T=6-21, average T = 17

As far as I understand, for long panels (N>T), robust standard errors in xtreg take care of autocorrelation, whereas for wide panels (N<T), one should use xtpcse/xtgls and use the option corr(ar1). Now, my question is: When can a panel be considered long enough? In situation number 3, I think I should use xtpcse because, on average, N<T, but what about situations 1 and 2, where T is not much larger than N? Should I consider them long panels? Do robust standard errors also take care of autocorrelation in these situations?

I hope my question is sufficiently clear.

Thank you,
Simone

[Carlo Lazzaro]

Simone:
welcome to this forum.
I would check the literature in your research field and see whether macroeconometric panel dataset of the very same size are treated as short or long panel datasets.
That said, my two-cent reply follows:
1) I would go -xtreg- in 1) and 2) with cluster robust standard errors (that, as you state, take both heteroskedsticity and autocorrelation into account);
2) I woud go -xtregar- in 3).

[Simone Tonelli]

Hi Carlo,

Thank you so much for your reply! Many authors in my and neigboring fields using PCSE do not seem concerned with the relative lengths of N and T and use them even in what I would define as wide datasets (e.g., N=23, T=6). So, I guess I have to choose between what seems to be a standard approach in the field or defend a different choice on the grounds of N and T relative sizes. Could you recommend a reference for that?

As a follow-up question, I wonder what the implication of using PCSE in wide datasets is. Does it make the standard errors unnecessarily conservative or completely bias the estimates?

All the best,
Simone

[Carlo Lazzaro]

Simone:
I can't advise on that as I am not familiar with macroeconometrics.
I think that @Jan Ditzen can be helpful if chiming in this thread.
That said, I would stick with what is considered mainstrean in your research field.
-xtpcse-affects standard errors only:

. webuse grunfeld

. xtset company year, yearly

Panel variable: company (strongly balanced)
 Time variable: year, 1935 to 1954
         Delta: 1 year

. xtpcse invest mvalue kstock

Linear regression, correlated panels corrected standard errors (PCSEs)

Group variable:   company                       Number of obs     =        200
Time variable:    year                          Number of groups  =         10
Panels:           correlated (balanced)         Obs per group:
Autocorrelation:  no autocorrelation                          min =         20
                                                              avg =         20
                                                              max =         20
Estimated covariances      =        55          R-squared         =     0.8124
Estimated autocorrelations =         0          Wald chi2(2)      =     637.41
Estimated coefficients     =         3          Prob > chi2       =     0.0000

------------------------------------------------------------------------------
             |           Panel-corrected
      invest | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
      mvalue |   .1155622   .0072124    16.02   0.000      .101426    .1296983
      kstock |   .2306785   .0278862     8.27   0.000     .1760225    .2853345
       _cons |  -42.71437   6.780965    -6.30   0.000    -56.00482   -29.42392
------------------------------------------------------------------------------

. xtgls invest mvalue kstock

Cross-sectional time-series FGLS regression

Coefficients:  generalized least squares
Panels:        homoskedastic
Correlation:   no autocorrelation

Estimated covariances      =         1          Number of obs     =        200
Estimated autocorrelations =         0          Number of groups  =         10
Estimated coefficients     =         3          Time periods      =         20
                                                Wald chi2(2)      =     866.14
Log likelihood             = -1191.802          Prob > chi2       =     0.0000

------------------------------------------------------------------------------
      invest | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
      mvalue |   .1155622   .0057918    19.95   0.000     .1042105    .1269138
      kstock |   .2306785    .025284     9.12   0.000     .1811227    .2802342
       _cons |  -42.71437   9.440069    -4.52   0.000    -61.21656   -24.21217
------------------------------------------------------------------------------

.

[Simone Tonelli]

That's great. Thank you for the helpful advice!

Have a nice day,
Simone

[Simone Tonelli]

Hi Carlo,

Following up on our exchange above, do you have a reference discussing that xtpcse/xtregar with AR correction is better suited for short panels and xtreg with robust standard errors is suitable for long panels?

Thanks again!

Simone